<commit_before># Espalhamento De Luz Estático
===============================

## Resumo
### Wikipedia

* **Static light scattering** is a technique in physical chemistry that measures the **intensity of the scattered light** to obtain the **average molecular weight** of a macromolecule like a polymer or a protein in solution. 
* Measurement of the scattering intensity at many angles allows calculation of the [..] **radius of gyration**. By measuring the scattering intensity for many samples of various concentrations, **the second virial coefficient**, can be calculated.
*  For static light scattering experiments, a **high intensity monochromatic light**, usually a laser, is launched in a solution containing the macromolecules. One or many detectors are used to measure the scattering intensity at one or many angles. 
* The angular dependence is required to obtain accurate measurements of both molar mass and size for all macromolecules of radius above 1-2% the incident wavelength. 
* Hence simultaneous measurements at several angles relative to the direction of incident light [...] **multi-angle light scattering (MALS)** [...] is generally regarded as the **standard implementation of static light scattering**
* All commercial instruments are calibrated using a strong, known scatterer like toluene since the Rayleigh Ratio of toluene and a few other solvents were measured using an absolute light scattering instrument.
* For a light scattering instrument composed of many detectors placed at various angles, all the detectors need to respond the same way. Usually detectors will have slightly different quantum efficiency, different gains and are looking at different geometrical scattering volumes. In this case a **normalization of the detectors is absolutely needed**. To normalize the detectors, a measurement of a pure solvent is made first.
*For polymers and polymer complexes which are of a monodisperse nature [...], a **Zimm plot** is a conventional means of deriving the parameters such as **radius of gyration**, **molecular mass** and the **second virial coefficient**

### <NAME>/Carraher
* This technique is based on the optical heterogeneity of polymer solutions and was developed by Nobel laureate *<NAME>* in 1944.
* For **small particles** the light is scattered equally, independent of the angle of the observer to the incoming light. For **larger particles** the intensity of scattered light varies with respect to the angle of the observer to the incoming light.

### Apostila sobre Espectometria
* The **intensity** of the scattered light depends on the **polarizability** and the polarizability depends on the **molecular weight**
* This result contrasts to colligative properties, such as osmotic pressure, which only depended on number of particles and therefore gave the number average molecular weight
* For polymer solutions, this dependence on size can be used to measure the **radius of gyration** of the polymer molecule
* Nonideality complicates the data analysis, but, like osmotic pressure, allows you to determining a **virial coefficient**, A2
* *Rayleigh theory* applies to **small particles**. By small particles, we mean particles whose size is much less than λ or the wavelength of the light that is being scattered
* A light scattering theory known as the **Rayleigh-Gans** theory was developed to extend Rayleigh theory to particles that are not optically small [...] This correction technique is important for analyzing results on **polymer solutions**
* The other [extrapolation of the analysis] is an extrapolation to zero concentration to remove the effect of non-ideal solutions

-----------------------------------------------------------------------------------------

* The higher a particle’s **polarizability** the higher will be the magnitude of the **dipole moment induced** by a given electromagnetic field
* The induced dipole moment will radiate light **in all directions**
* Boa explicação intuitiva da equação para a Intensidade da Luz Espalhada baseando-se na polarizabilidade da partícula segundo a Teoria de Rayleigh
* The above results are for incident light polarized in the z direction. Experiments, however, are usually done with unpolarized light. We can account for unpolarized incident light by summing the intensity of equal parts of incident light polarized in both the z direction and the y direction.
* The light scattering intensity **depends on scattering angle** [...] The maximum scattering intensity is at θ = 0. The minimum scattering intensity is at θ = 90 [...] the scattering intensity at angle θ is equal to the scattering intensity at angle 180 − θ
* As a function of λ, the scattered intensity is proportional *1/λ⁴* . This strong wavelength dependence makes short wavelength light scatter more than long wavelength light. **This effect explains why the sky is blue**
* **At sunset** you normally do look in the direction of the sun and θ is zero or near zero. Because **blue light is scattered away**, you are left with the red light and sunsets appear red.

-----------------------------------------------------------------------------------------

* The polarizability can be thought of as a **difference in the index of refraction** between the polymer and the solvent. In other words light scattering only occurs in mediums that have an inhomogeneous index of refraction
* if the index of refraction of the solvent and of the polymer are the same then *dn0/dc* will be zero and there would be no polarizability and therefore no scattered light
* In a given scattering experiment, *I0* and *r* will be fixed and we will measure *i0θ* . These measured quantities can be combined into one quantity called the **Rayleigh ratio** *R0θ* [...] The advantage of the Rayleigh ratio is that it is **independent** of the **incident light intensity** and the **distance** to the scattered light detector
* K is therefore a **system constant** that is **independent** of the concentration of the solution and the molecular weight of the **polymer**
* For a dilute, polydisperse polymer solution, the total Rayleigh ratio can be written as a **sum of the Rayleigh ratios** for scattering of polymers of each possible molecular weight

-----------------------------------------------------------------------------------------

### Resumo da Aula (Lucaix):
* Interação luz-polímero, polarizabilidade da molécula;
* Incremento do índice de refração *dn/dc* ;
* Purificação dos solventes e soluções na preparação da amostra;
* Coeficientes do Virial (servem p determinar forma e tamanho dos bagúio);
* Diagram<NAME>, raio de Giro;

## Referências
[Wikipedia](https://en.wikipedia.org/wiki/Static_light_scattering)
<commit_msg>Atualização do README até, incluindo, seção 7.5<commit_after># Espalhamento De Luz Estático

## Resumo
### Wikipedia

* **Static light scattering** is a technique in physical chemistry that measures the **intensity of the scattered light** to obtain the **average molecular weight** of a macromolecule like a polymer or a protein in solution. 
* Measurement of the scattering intensity at many angles allows calculation of the [..] **radius of gyration**. By measuring the scattering intensity for many samples of various concentrations, **the second virial coefficient**, can be calculated.
*  For static light scattering experiments, a **high intensity monochromatic light**, usually a laser, is launched in a solution containing the macromolecules. One or many detectors are used to measure the scattering intensity at one or many angles. 
* The angular dependence is required to obtain accurate measurements of both molar mass and size for all macromolecules of radius above 1-2% the incident wavelength. 
* Hence simultaneous measurements at several angles relative to the direction of incident light [...] **multi-angle light scattering (MALS)** [...] is generally regarded as the **standard implementation of static light scattering**
* All commercial instruments are calibrated using a strong, known scatterer like toluene since the Rayleigh Ratio of toluene and a few other solvents were measured using an absolute light scattering instrument.
* For a light scattering instrument composed of many detectors placed at various angles, all the detectors need to respond the same way. Usually detectors will have slightly different quantum efficiency, different gains and are looking at different geometrical scattering volumes. In this case a **normalization of the detectors is absolutely needed**. To normalize the detectors, a measurement of a pure solvent is made first.
*For polymers and polymer complexes which are of a monodisperse nature [...], a **Zimm plot** is a conventional means of deriving the parameters such as **radius of gyration**, **molecular mass** and the **second virial coefficient**

### <NAME>/Carraher
* This technique is based on the optical heterogeneity of polymer solutions and was developed by <NAME> *<NAME>* in 1944.
* For **small particles** the light is scattered equally, independent of the angle of the observer to the incoming light. For **larger particles** the intensity of scattered light varies with respect to the angle of the observer to the incoming light.

### Apostila sobre Espectometria
* The **intensity** of the scattered light depends on the **polarizability** and the polarizability depends on the **molecular weight**
* This result contrasts to colligative properties, such as osmotic pressure, which only depended on number of particles and therefore gave the number average molecular weight
* For polymer solutions, this dependence on size can be used to measure the **radius of gyration** of the polymer molecule
* Nonideality complicates the data analysis, but, like osmotic pressure, allows you to determining a **virial coefficient**, A2
* *Rayleigh theory* applies to **small particles**. By small particles, we mean particles whose size is much less than λ or the wavelength of the light that is being scattered
* A light scattering theory known as the **Rayleigh-Gans** theory was developed to extend Rayleigh theory to particles that are not optically small [...] This correction technique is important for analyzing results on **polymer solutions**
* The other [extrapolation of the analysis] is an extrapolation to zero concentration to remove the effect of non-ideal solutions

-----------------------------------------------------------------------------------------

* The higher a particle’s **polarizability** the higher will be the magnitude of the **dipole moment induced** by a given electromagnetic field
* The induced dipole moment will radiate light **in all directions**
* Boa explicação intuitiva da equação para a Intensidade da Luz Espalhada baseando-se na polarizabilidade da partícula segundo a Teoria de Rayleigh
* The above results are for incident light polarized in the z direction. Experiments, however, are usually done with unpolarized light. We can account for unpolarized incident light by summing the intensity of equal parts of incident light polarized in both the z direction and the y direction.
* The light scattering intensity **depends on scattering angle** [...] The maximum scattering intensity is at *θ = 0* . The minimum scattering intensity is at *θ = 90* [...] the scattering intensity at angle *θ* is equal to the scattering intensity at angle *180 − θ*
* As a function of λ, the scattered intensity is proportional *1/λ⁴* . This strong wavelength dependence makes short wavelength light scatter more than long wavelength light. **This effect explains why the sky is blue**
* **At sunset** you normally do look in the direction of the sun and *θ* is zero or near zero. Because **blue light is scattered away**, you are left with the red light and sunsets appear red.

-----------------------------------------------------------------------------------------

* The polarizability can be thought of as a **difference in the index of refraction** between the polymer and the solvent. In other words light scattering only occurs in mediums that have an inhomogeneous index of refraction
* if the index of refraction of the solvent and of the polymer are the same then *dn0/dc* will be zero and there would be no polarizability and therefore no scattered light
* In a given scattering experiment, *I0* and *r* will be fixed and we will measure *i0θ* . These measured quantities can be combined into one quantity called the **Rayleigh ratio** *R0θ* [...] The advantage of the Rayleigh ratio is that it is **independent** of the **incident light intensity** and the **distance** to the scattered light detector
* K is therefore a **system constant** that is **independent** of the concentration of the solution and the molecular weight of the **polymer**
* For a dilute, polydisperse polymer solution, the total Rayleigh ratio can be written as a **sum of the Rayleigh ratios** for scattering of polymers of each possible molecular weight

-----------------------------------------------------------------------------------------

* As done with osmotic pressure, the possibility of **non-ideal solutions** is handled by **adding virial coefficients** and concentration terms to the ideal result
* The only difference between the *A2* in osmotic pressure and the *A2* in light scattering is that the **light scattering _A2_** is formally a **weight-average virial coefficient**. Besides that difference, the light scattering *A2* gives similar information, notably information about the quality of the solvent.
* This extrapolation, however, ignores any possible large particle size effects The extrapolated *Mw* will therefore be in error

-----------------------------------------------------------------------------------------

* If a particle is not small compared to the wavelength of light, the light can scatter from **different parts** of the particle [...] traveling **different path lengths**
* The amount of intensity reduction or the amount of destructive interference depends on the scattering angle. At *θ* equal to zero, the path lengths will always be identical. As θ
increases, the interference will increase reaching a maximum and *θ = 180◦*
* scattering diagram shows the effect of large particles and now shows **asymmetry in scattering**; i.e., the back scattering intensity is much reduced from the forward scattering intensity
* To correct for large particles, we merely need to do the light scattering experiments at zero scattering angle. [However,] At *θ = 0* most light will be transmitted light that is **not scattered**
* Instead, we must do experiments at *θ > 0* and extrapolate to *θ = 0* . We thus do a second extrapolation, an **extrapolation to zero scattering angle**
* *P(θ)* is the ratio between the actual scattering ( *iθ* ) and the scattering that
would occur off small particles ( *i0θ* )
* *P(0) = 1* [...] and *P(θ) < 1* for all other *θ* (destructive interference can only cause a reduction in intensity). 
* The larger effect on back scattering than on forward scatter means that *P(θ < 90) > P(180 − θ)*
* A extrapolação dita acima consiste basicamente em escever *Rθ* em função de *P(θ)* tomando como base a teoria para partículas pequenas (aí está a extrapolação para *P(θ) = 0* )
* De alguma forma mágica ele expande ainda mais a equação e chega inesperadamente no **Raio de Giração** *Rg*

-----------------------------------------------------------------------------------------

* To handle both non-ideal solutions and large particle effects, we need to do two extrapolations. First, we introduce non-ideal solution effects into the large particle analysis in the previous section. Instead of using *P(θ)* to **correct** the ideal solution result, we use it to correct the **non-ideal** solution result

### Resumo da Aula (Lucaix):
* Interação luz-polímero, polarizabilidade da molécula;
* Incremento do índice de refração *dn/dc* ;
* Purificação dos solventes e soluções na preparação da amostra;
* Coeficientes do Virial (servem p determinar forma e tamanho dos bagúio);
* Diagrama de Zimm, raio de Giro;

## Referências
[Wikipedia](https://en.wikipedia.org/wiki/Static_light_scattering)

{'fraction_non_alphanumeric': 0.10351224338362602, 'fraction_numerical': 0.003586445708632204, 'mean_word_length': 3.8743218806509945, 'pattern_counts': {'":': 0, '<': 11, '<?xml version=': 0, '>': 11, 'https://': 2, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
{'dir': 'git-commits-cleaned', 'id': '1386208', 'n_tokens_mistral': 3787, 'n_tokens_neox': 3495, 'n_words': 2273}