= Solution
The three solvent conditions describe effective interactions between segments of a generic <polymer>. In a <good solvent>, solvent contacts favor a swollen, self-avoiding coil with positive <excluded volume>. At a <theta solvent> condition, leading pair repulsion and attraction cancel; the chain has approximately ideal random-walk statistics. In a <poor solvent>, effective attraction contracts the chain, eventually producing a dense <polymer globule> for a sufficiently long chain.
For $N$ statistical segments of <length> $a$, the <radius of gyration> has the scaling
$$
\boxed{R_g\sim\begin{cases}
aN^{3/5},&\text{good solvent},\\
aN^{1/2},&\text{theta/ideal solvent},\\
aN^{1/3},&\text{dense poor-solvent globule}.
\end{cases}}
$$
The good-solvent power $3/5$ is the <Flory approximation>; the asymptotic three-dimensional exponent is closer to $0.588$. In the ideal <freely jointed chain>, the more precise result is $R_g^2\simeq Na^2/6$, whereas the end-to-end <mean> square is $Na^2$. Scaling notation suppresses those geometry-dependent factors. The globule power follows from a <volume> proportional to $N$, and presumes a dense collapsed state away from the theta crossover. The dilute condition excludes overlap with other chains; it does not eliminate contacts between distant segments of the same chain.
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